ACE TRIG Final EXAM REVIEW
Multiple Choice
Identify the letter of the choice that best completes the statement or answers the question.
____
____
____
____
____
1. Change
to degrees, minutes, and seconds.
a. 250° 19´ 20´´
c. 250° 20´ 20´´
b.
31´ 12´´
d. 250° 17´ 19´´
2. Write ° ´ ´´ as a decimal to the nearest thousandth.
a.
°
c.
°
b.
°
d.
°
3. Find the least positive angle measurement that is coterminal with
a.
°
c.
°
b.
°
d.
°
4. Change 3.94 radians to degree measure. Round to the nearest tenth.
a.
c.
b.
d.
5. Change
to radian measure in terms of .
a. 35
c. 35
b.
54
35
d.
18
____
____
36
35
72
6. Find the polar coordinates of (6 3 , 6) for r > 0.
a.
c.
(12,
)
(
b.
(–12,
°.
d.
)
, 12)
(6,
)
7. Find the rectangular coordinates of
a.
c.
b.
d.
____
8. Determine the polar form of the complex number
. Express the angle  in degrees, where
round numerical entries in the answer to two decimal places.
a.
c.
b.
d.
____
9. Write
places.
a.
b.
in standard form
____ 10. Given
the answer to two decimal places.
a.
b.
, and
Round numerical entries in the answer to two decimal
c.
d.
and
find and simplify
c.
d.
Round numerical entries in
____ 11. Find
a. 9i
b. 8i
. Express the result in rectangular form.
c. 6i
d. 7i
_____12. Find the position vector for the vector having initial point P and terminal point Q.
P = (0, 0, 0) and Q = (2, -2, -3)
a. v = -2i + 2j + 3k
b. v = 2i - 2j - 3k
c. v = 2i - 2j + 3k
d. v = -3i - 2j + 2k
____ 13. Find the position vector for the vector having initial point P and terminal point Q.
P = (4, 2, -4) and Q = (2, 0, 1)
a. v = -2i - 2j + 5k
b. v = 2i + 2j - 5k
____ 14. Find
.
v = 3i + 4j + 2k
a.
b. 3
____ 15. Find
c. v = 6i - 2j - 5k
d. v = -3i - 2j + 6k
c.
d. 5
.
v = -3i - 6j + 3k
a. 3
b. 3
c. 6
d. 2
____ 16. Perform the indicated operation.
v = 5i - 6j - 3k and w = 3i - 4j - 2k
Find 3v + 2w.
a. 8i - 10j - 5k
b. 11i - 14j - 7k
c. 18i - 22j - 11k
d. 21i - 26j - 13k
____ 17. Find the dot product v • w.
v = i + j and w = i + j - k
a. 2
b. -2
c. 1
d. 3
____ 18. Find the dot product v • w.
v = 2i + j + 3k and w = i + 2j - 2k
a. -6
b. -7
c. 2
d. -2
____ 19. Find the indicated cross product.
v = -4i + 2j + k, w = -6i + 5j - k
Find v  w.
a. 3i + 2j - 32k
b. -7i - 10j - 8k
c. 7i + 10j + 22k
d. -8i + 7j + 10k
____ 20. Find the indicated cross product.
v = 5i + 2j, w = 2i - 2j - 3k
Find v  w.
a. -14i + 6j - 15k
b. -6i + 15j - 6k
c. -6i + 15j - 14k
d. -6i - 6j + 14k
Short Answer
21. Find the least positive angle measurement that is coterminal with
.
22. In right triangle ABC, A = 15, c = 37, and C is the right angle. Solve the triangle. Round to the nearest tenth, if
necessary.
23. Find sec 47° to four decimal places.
24. Solve triangle ABC given that A = °, B =
°, and b = 12.
25. Given a triangle with b = , c = , and A =
°, what is the length of a? Round to the nearest tenth.
26. Change
27. Change
radians to degree measure.
to radian measure in terms of
28. Verify that
is an identity.
29. Verify that
30. Verify that
31. Graph the polar equation
is an identity.
is an identity.
Graph r=5.
32. Find the polar coordinates of (–6, 6 3 ) for r > 0.
33. Find the rectangular coordinates of
.
34. Find the product. Then express the result in rectangular form.
35.
36.
37.
38.
Find
. Express the result in rectangular form.
If two vectors are orthogonal, what will their dot product equal?
Find the inverse of y= cos 3x.
Evaluate sin(Cos-1 ½ )
Graph. State the amplitude, period, phase shift, and vertical translation as applicable.
39. y = tan x
40. y = cot x
41. y = sec x
42 y = csc x
44. y  3  5cos   
1
2
43. y  5  2sin  4  2 
 

16 
45. Write the equation of this graph.
Use the following for 46-49
8
17
5
cos x 
13
cos z 
15
17
12
sin x 
13
sin z 
46. cos(x+z)
15
8
12
tan x 
5
tan z 
47. tan(x+z)
48. cos 2x
49. sin 2x
Find general solution in terms of k and find all solutions between 0 and 360.
50. 2sin  1  0
51. cos 2 x  cos x  2  0
52. sin 2 x  4sin x  0
53. A model rocket is fired from ground level with an initial velocity of 80 feet per second at a launch angle of 75°.
Write the parametric equation.
How far horizontally will the rocket have traveled in 1.5 seconds?
How long will it take the rocket to land?
54. A tree casts a 45 foot shadow. The angle of elevation of the sun is 57°. Sketch a picture. Label the angle of elevation.
55. Resolve a vector with magnitude 10 and direction 220° with the horizontal into horizontal and vertical components.
56. Write the slope-intercept equation of the line with these parametric equations:
x= t+5 y= 4t -1
Honors Precalculus Final Exam Review B
Answer Section
MULTIPLE CHOICE
1. ANS:
STO:
KEY:
2. ANS:
STO:
KEY:
3. ANS:
TOP:
4. ANS:
STO:
KEY:
5. ANS:
STO:
KEY:
6. ANS:
TOP:
7. ANS:
STO:
KEY:
8. ANS:
STO:
KEY:
9. ANS:
STO:
KEY:
10. ANS:
TOP:
KEY:
11. ANS:
TOP:
KEY:
12. ANS:
OBJ:
STO:
TOP:
KEY:
B
OBJ: 5-1.1 Convert decimal degree measures to degrees¸ minutes¸ and seconds.
IN PC.4
TOP: Convert decimal degree measures to degrees¸ minutes¸ and seconds.
Angle Measures, Degree Measures
C
OBJ: 5-1.1 Convert decimal degree measures to degrees¸ minutes¸ and seconds.
IN PC.4
TOP: Convert decimal degree measures to degrees¸ minutes¸ and seconds.
Angle Measures, Degree Measures
A
OBJ: 5-1.4 Identify angles that are coterminal with a given angle.
Identify angles that are coterminal with a given angle.
KEY: Coterminal Angles
C
OBJ: 6-1.1 Change radian measures to degree measures.
IN PC.4.2, IN PC.4
TOP: Change radian measures to degree measures.
Angle Measures, Degree Measures, Radian Measures
C
OBJ: 6-1.2 Change degree measures to radian measures.
IN PC.4.2, IN PC.4
TOP: Change degree measures to radian measures.
Angle Measures, Degree Measures, Radian Measures
C
OBJ: 6-2.1 Find linear and angular velocity.
Find linear and angular velocity.
KEY: Linear Velocity, Angular Velocity
A
OBJ: 9-3.1 Convert from rectangular coordinates to polar coordinates.
IN PC.6.1
TOP: Convert from rectangular coordinates to polar coordinates.
Rectangular Coordinates, Polar Coordinates
C
OBJ: 9-3.2 Convert from polar coordinates to rectangular coordinates.
IN PC.6.1
TOP: Convert from polar coordinates to rectangular coordinates.
Polar Coordinates, Rectangular Coordinates
C
OBJ: 9-6.2 Convert complex numbers from rectangular form to polar form.
IN PC.6.4
TOP: Convert complex numbers from rectangular form to polar form.
Complex Numbers, Rectangular Form, Polar Form
C
OBJ: 9-6.3 Convert complex numbers from polar form to rectangular form.
Convert complex numbers from polar form to rectangular form.
Complex Numbers, Rectangular Form, Polar Form
B
OBJ: 9-7.1 Find the product and quotient of complex numbers in polar form.
Find the product and quotient of complex numbers in polar form.
Multiply Complex Numbers, Divide Complex Numbers, Complex Numbers, Polar Form
B
9-8.1 Find powers and roots of complex numbers in polar form using De Moivre's Theorem.
IN PC.6.5
Find powers and roots of complex numbers in polar form using De Moivre's Theorem.
Powers of Complex Numbers, Roots of Complex Numbers, Polar Form, De Moivre's Theorem
SHORT ANSWER
13. ANS:
OBJ: 5-1.4 Identify angles that are coterminal with a given angle.
TOP: Identify angles that are coterminal with a given angle.
KEY: Coterminal Angles
14. ANS:
B = 75, a = 9.6, b = 35.7
OBJ: 5-5.3 Solve right triangles.
STO: IN PC.3
KEY: Right Triangles, Solve Right Triangles
TOP: Solve right triangles.
15. ANS:
A = 75, b = 3.6, c = 13.5
OBJ: 5-5.3 Solve right triangles.
STO: IN PC.3
KEY: Right Triangles, Solve Right Triangles
16. ANS:
OBJ:
STO:
TOP:
KEY:
17. ANS:
15
TOP: Solve right triangles.
5-6.1 Solve triangles by using the Law of Sines if the measures of two angles and a side are given.
IN PC.3.2, IN PC.3
Solve triangles by using the Law of Sines if the measures of two angles and a side are given.
Solve Triangles, Law of Sines
OBJ: 5-8.1 Solve triangles using the Law of Cosines.
TOP: Solve triangles using the Law of Cosines.
18. ANS:
STO: IN PC.3.1, IN PC.3.2, IN PC.3
KEY: Solve Triangles, Law of Cosines
OBJ: 6-1.1 Change radian measures to degree measures.
TOP: Change radian measures to degree measures.
KEY: Angle Measures, Degree Measures, Radian Measures
19. ANS:
STO: IN PC.4.2, IN PC.4
OBJ: 6-1.2 Change degree measures to radian measures.
TOP: Change degree measures to radian measures.
KEY: Angle Measures, Degree Measures, Radian Measures
20. ANS:
145.77 cm/s
STO: IN PC.4.2, IN PC.4
OBJ: 6-2.1 Find linear and angular velocity.
KEY: Linear Velocity, Angular Velocity
21. ANS:
TOP: Find linear and angular velocity.
OBJ:
STO:
TOP:
KEY:
22. ANS:
7-2.1 Use the basic trigonometric identities to verify other identities.
IN PC.5.2, IN PC.5
Use the basic trigonometric identities to verify other identities.
Trigonometric Identities, Verify Identities
OBJ:
STO:
TOP:
KEY:
23. ANS:
7-2.1 Use the basic trigonometric identities to verify other identities.
IN PC.5.2, IN PC.5
Use the basic trigonometric identities to verify other identities.
Trigonometric Identities, Verify Identities
OBJ:
STO:
TOP:
KEY:
24. ANS:
7-2.1 Use the basic trigonometric identities to verify other identities.
IN PC.5.2, IN PC.5
Use the basic trigonometric identities to verify other identities.
Trigonometric Identities, Verify Identities
OBJ: 9-1.2 Graph simple polar equations.
STO: IN PC.6.3
TOP: Graph simple polar equations.
KEY: Polar Equations, Graph Polar Equations
25. ANS:
(12,
)
OBJ: 9-3.1 Convert from rectangular coordinates to polar coordinates.
STO: IN PC.6.1
TOP: Convert from rectangular coordinates to polar coordinates.
KEY: Rectangular Coordinates, Polar Coordinates
26. ANS:
OBJ: 9-3.2 Convert from polar coordinates to rectangular coordinates.
STO: IN PC.6.1
TOP: Convert from polar coordinates to rectangular coordinates.
KEY: Polar Coordinates, Rectangular Coordinates
27. ANS:
–3–3
3i
OBJ: 9-7.1 Find the product and quotient of complex numbers in polar form.
TOP: Find the product and quotient of complex numbers in polar form.
KEY: Multiply Complex Numbers, Divide Complex Numbers, Complex Numbers, Polar Form
28. ANS:
–16 + 16i
OBJ:
STO:
TOP:
KEY:
9-8.1 Find powers and roots of complex numbers in polar form using De Moivre's Theorem.
IN PC.6.5
Find powers and roots of complex numbers in polar form using De Moivre's Theorem.
Powers of Complex Numbers, Roots of Complex Numbers, Polar Form, De Moivre's Theorem